Fractal visionaries and enthusiasts:  

Today's image lies very deep in the parent fractal that comes about when 0.1 part of Z^(4.4) is combined with 2 parts of Z^(0.4) and straight C is added on each iteration.  This parent resembles a Mandelbrot set facing northeast with a large triangular area sprouting behind it from its East Valley area.  Today's scene is located in the northwest valley forming the entrance to this triangular area.

The name "In Deep Territory" refers to the unusual magnitude of the image, one of the greatest of all time.

The rating of an 8 reflects my opinion of the image at the time I rated it.  I may soon shift to an more informative rating system that gives two ratings, one for the artistic value, the other for the mathematical interest.

A good part of the artistic effect was achieved by rendering the image with the inside set to 'fmod'.  The magnitude of over 2.5*(10^13) is at the verge of resolution breakdown.  In fact, the breakdown is already becoming visible along some of the sharp edges.

Luckily, the image calculates in 3-1/2 minutes, surprisingly fast for a scene that uses the 'fmod' feature.  And the web sites are always there for instant enjoyment.

Another absolutely perfect day prevailed here at Fractal Central today.  The few angel-hair cirrus clouds that appeared in the morning, and the few cotton-puff cumulus clouds that popped up over the ridges in the afternoon did nothing but add to the perfection.  The temperature of 73F 23C and gentle southeast wind were also perfect.  The fractal cat admired the outdoor conditions . . . from the inside.  The fractal humans also admired the outdoor conditions.

The next FOTD will be posted in a number of hours.  Until that number passes, take care, and I am still waiting for someone to solve the very interesting and quite puzzling 'Boltzmann brain' paradox, which currently has physicists pondering and rational skeptics a bit concerned also.  I'll forget the convoluted line of thought about entropy that led to the problem, since it is on the internet.  At this time, I'll merely state that either the existence of the universe involves more than pure blind chance, or the universe is filled with disembodied 'Boltzmann brains' which somehow can exist and be conscious while floating in empty space.

The apparently 'logical' deduction is that, if the universe is merely a random accident, then it is many googols of times more likely that, instead of existing in a real physical universe, I am a pathetic deluded Boltzmann brain, floating in empty space and imagining everything I have ever experienced, including the physical world and everything else that appears to be so real.  I doubt that this is true, but, despite convoluted claims to the contrary, no one has yet been able to show beyond doubt that it is untrue without invoking an intelligence of some kind to eliminate the random element.  And we know what rational scientific skeptics think of the idea of 'God'.

Jim Muth
jimmuth@earthlink.net


START PARAMETER FILE=======================================

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  formulaname=MandAutoCritInZ function=ident
  center-mag=-1.122707213001586/-0.1067224794760605/\
  2.545255e+013/1/-15/0 params=0.1/4.4/2/0.4/0/0
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frm:MandAutoCritInZ {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }

END PARAMETER FILE=========================================